Puzzle 035

Puzzle 035: Guess Stars

A bored bartender plays a game that would be loved in the Fallout universe. Five bottle caps are placed on the table with the logos facing up. She closes her eyes and starts randomly flipping over the caps, and when she does her 25th flip, she covers one cap and asks her patron if the cap is logo-up or logo-down. Looking at the other four caps, you're asked to figure it out.

The easiest way to solve this one (if you want to count out the number of flips) is to just assume she flipped her hidden one the maximum number of times. That is: with four caps showing, and two logo-down, you know she flipped those two once each. That leaves 23 flips... so what would happen if she just flipped that last cap 23 times?